A245160 Number of length n 0..5 arrays with new values introduced in order from both ends.

1, 1, 2, 4, 9, 23, 65, 199, 654, 2296, 8569, 33825, 140580, 612890, 2794159, 13280627, 65597882, 335521900, 1770176005, 9593485125, 53183385680, 300371056446, 1721926382427, 9987133305239, 58446578859494, 344361988828048

Offset

1,3

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 26*a(n-1) - 290*a(n-2) + 1820*a(n-3) - 7073*a(n-4) + 17618*a(n-5) - 28060*a(n-6) + 27480*a(n-7) - 14976*a(n-8) + 3456*a(n-9) for n>10.

Empirical g.f.: x*(1 - 25*x + 266*x^2 - 1578*x^3 + 5738*x^4 - 13236*x^5 + 19385*x^6 - 17565*x^7 + 9271*x^8 - 2381*x^9) / ((1 - x)^2*(1 - 2*x)^2*(1 - 3*x)^2*(1 - 4*x)^2*(1 - 6*x)). - Colin Barker, Nov 03 2018

Example

Some solutions for n=7:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....1....1....1....1....1....1....1....0....1....0....1....1....1....1....0
..1....2....1....0....0....0....0....0....1....2....1....0....0....2....1....1
..0....2....0....0....2....1....0....1....2....2....2....0....1....2....2....2
..2....2....0....0....0....0....0....0....0....0....1....1....1....1....2....2
..1....1....1....0....1....1....1....0....1....1....0....0....0....0....1....1
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

Crossrefs

Column 5 of A245163.

Sequence in context: A014137 A245158 A245159 * A245161 A245162 A007476

Adjacent sequences: A245157 A245158 A245159 * A245161 A245162 A245163

Keyword

nonn

Author

R. H. Hardin, Jul 12 2014

Status

approved